NZMATH  1.2.0
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nzmath.intresidue.IntegerResidueClassRing Class Reference
Inheritance diagram for nzmath.intresidue.IntegerResidueClassRing:
Collaboration diagram for nzmath.intresidue.IntegerResidueClassRing:

Public Member Functions

def __init__ (self, modulus)
def __repr__ (self)
def __str__ (self)
def __hash__ (self)
def card (self)
def getInstance (cls, modulus)
def createElement (self, seed)
def getCharacteristic (self)
def __contains__ (self, elem)
def isfield (self)
def __eq__ (self, other)
def __ne__ (self, other)
def issubring (self, other)
def issuperring (self, other)
- Public Member Functions inherited from nzmath.ring.CommutativeRing
def __init__ (self)
def getQuotientField (self)
def isdomain (self)
def isnoetherian (self)
def isufd (self)
def ispid (self)
def iseuclidean (self)
def registerModuleAction (self, action_ring, action)
def hasaction (self, action_ring)
def getaction (self, action_ring)
- Public Member Functions inherited from nzmath.ring.Ring
def getCommonSuperring (self, other)

Public Attributes

- Public Attributes inherited from nzmath.ring.CommutativeRing

Static Public Attributes

def isdomain = isfield
def isnoetherian = isfield
def isufd = isfield
def ispid = isfield
def iseuclidean = isfield


 one = property(_getOne, None, None, "multiplicative unit.")
 zero = property(_getZero, None, None, "additive unit.")

Private Member Functions

def _getOne (self)
def _getZero (self)

Private Attributes


Static Private Attributes

dictionary _instances = {}

Detailed Description

IntegerResidueClassRing is also known as Z/mZ.

Definition at line 218 of file

Constructor & Destructor Documentation

◆ __init__()

def nzmath.intresidue.IntegerResidueClassRing.__init__ (   self,
The argument modulus m specifies an ideal mZ.

Definition at line 225 of file

Member Function Documentation

◆ __contains__()

def nzmath.intresidue.IntegerResidueClassRing.__contains__ (   self,

◆ __eq__()

◆ __hash__()

def nzmath.intresidue.IntegerResidueClassRing.__hash__ (   self)

◆ __ne__()

def nzmath.intresidue.IntegerResidueClassRing.__ne__ (   self,
Inequality test.

Reimplemented from nzmath.ring.Ring.

Definition at line 307 of file

◆ __repr__()

def nzmath.intresidue.IntegerResidueClassRing.__repr__ (   self)

◆ __str__()

def nzmath.intresidue.IntegerResidueClassRing.__str__ (   self)

◆ _getOne()

◆ _getZero()

◆ card()

def nzmath.intresidue.IntegerResidueClassRing.card (   self)
Return the cardinality of the ring.

Definition at line 245 of file

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ createElement()

def nzmath.intresidue.IntegerResidueClassRing.createElement (   self,
createElement returns an element of the ring with seed.

Reimplemented from nzmath.ring.Ring.

Definition at line 263 of file

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

Referenced by nzmath.finitefield.FiniteField.random_element(), and nzmath.finitefield.FiniteField.TonelliShanks().

◆ getCharacteristic()

def nzmath.intresidue.IntegerResidueClassRing.getCharacteristic (   self)
The characteristic of Z/mZ is m.

Reimplemented from nzmath.ring.Ring.

Definition at line 271 of file

References nzmath.intresidue.IntegerResidueClass.m, and nzmath.intresidue.IntegerResidueClassRing.m.

◆ getInstance()

def nzmath.intresidue.IntegerResidueClassRing.getInstance (   cls,
getInstance returns an instance of the class of specified

Definition at line 252 of file

References nzmath.finitefield.FinitePrimeField._instances, and nzmath.intresidue.IntegerResidueClassRing._instances.

◆ isfield()

def nzmath.intresidue.IntegerResidueClassRing.isfield (   self)
isfield returns True if the modulus is prime, False if not.
Since a finite domain is a field, other ring property tests
are merely aliases of isfield.

Reimplemented from nzmath.ring.CommutativeRing.

Definition at line 283 of file

References nzmath.intresidue.IntegerResidueClass.m, nzmath.intresidue.IntegerResidueClassRing.m, and

◆ issubring()

def nzmath.intresidue.IntegerResidueClassRing.issubring (   self,
Report whether another ring contains the ring as a subring.

Reimplemented from nzmath.ring.Ring.

Definition at line 310 of file

Referenced by nzmath.ring.Ring.getCommonSuperring(), nzmath.rational.RationalField.getCommonSuperring(), and nzmath.rational.IntegerRing.getCommonSuperring().

◆ issuperring()

Member Data Documentation

◆ _instances

◆ _one

◆ _zero

◆ isdomain

def nzmath.intresidue.IntegerResidueClassRing.isdomain = isfield

Definition at line 296 of file

◆ iseuclidean

def nzmath.intresidue.IntegerResidueClassRing.iseuclidean = isfield

Definition at line 300 of file

◆ isnoetherian

def nzmath.intresidue.IntegerResidueClassRing.isnoetherian = isfield

Definition at line 297 of file

◆ ispid

def nzmath.intresidue.IntegerResidueClassRing.ispid = isfield

Definition at line 299 of file

◆ isufd

def nzmath.intresidue.IntegerResidueClassRing.isufd = isfield

Definition at line 298 of file

◆ m

Property Documentation

◆ one

◆ zero = property(_getZero, None, None, "additive unit.")

Definition at line 336 of file

Referenced by nzmath.ring.Field.gcd(), and nzmath.matrix.MatrixRing.zeroMatrix().

The documentation for this class was generated from the following file: